Federer was making his first appearance at the tournament since winning the title in 2015.
After a first-round bye, he extended his Cincinnati winning streak to 11 matches since losing to Rafael Nadal in the 2013 quarterfinals.
"It doesn't feel like I have been away for so long here from Cincinnati,'' Federer said. "I guess the wheel keeps turning. It's not like I missed two years of tennis. It was a great pleasure to be back.''
The second-seeded Federer, refreshed from a month off after losing in the Wimbledon quarterfinals, became the tournament favorite when Nadal withdrew on Sunday night.
Pliskova moved into the second round by snapping a seven-match losing streak against Agnieszka Radwanska with a 6-3, 6-3 win.
"It means a lot because it was against her, and, like, you know, I never beat her,'' Pliskova said. "We played so many times. I think I always played her at her best level the matches before, so it was always tough.''
Kyrgios, a finalist last year in Cincinnati, overcame physical problems to fight off qualifier Denis Kudla for a 6-7 (2), 7-5, 7-6 (9) victory.
"This year has been tough,'' Kyrgios said. "I started the year very well. Then, obviously, I hurt my elbow. Then I had an ongoing hip injury. We have been definitely thinking about the options with my hip. You know, there is only so much you can do before you have to, you know, I guess, get surgery or something like that. You know, right now I'm just managing it.''
No. 11 seed David Goffin advanced with a 7-5, 6-3 win over Stefanos Tsitsipas, and Leonardo Mayer became the first player to reach the third round on the men's side with a 7-6 (7), 6-4 victory over 16th-seeded Lucas Pouille.
Fifth-seeded Elina Svitolina was tested by wild card Svetlana Kuznetsova before reaching the third round with a gritty 7-6 (1), 4-6, 6-4 win. Sixth-seeded Caroline Garcia also reached the third round with a 6-4, 6-5 win over wild card Victoria Azarenka, but 12th-seeded Daria Kasatkina suffered a first-round upset at the hands of qualifier Petra Martic, 4-6, 6-4, 6-3.
Information from The Associated Press was used in this report.